An Introductory Note on the Spectrum and Energy of Molecular Graphs
DOI:
https://doi.org/10.12723/mjs.41.3Keywords:
Molecular Graph, Spectrum, Energy, Spectral RadiusAbstract
Graph Theory is one branch of Mathematics that laid the foundations of the structural studies in Chemistry. The fact that every molecule or compound can be represented as a network of vertices (elements) and edges (bonds) provoked the question of the predictability of the physical and chemical properties of molecules and compounds. Spectrum, π-electron energy, Spectral Radius etc. are predictable using graph theoretical methods. This is an introductory paper about spectrum and energy of molecular graphs.
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[2] X. Li, Y. Shi and I. Gutman, Graph Energy. NY: Springer, 2012.
[3] R. Balakrishnan, ‘’The energy of a graph,” Linear Algebra and its Applications, vol. 387, pp. 287–295, 2004.
[4] R. B. Bapat, S. Pati, “Energy of a graph is never an odd integer,” Bulletin of Kerala Mathematics Association, vol. 1, pp. 129-132, 2011.
[5] C. Adiga, M. A. Sriraj, ``Color energy of a graph,’’ Proc. Jangjeon Mathematical Society, South Korea, Jan 2013.
[6] C. Adiga, A. Bayad, I. Gutman and S. A. Srinivas, “The Minimum Covering Energy of A Graph,” Kragujevac J. Sci. vol. 34, pp. 39–56, 2012.
[7] K. S. Betageri, “Reduced Color Energy of Graphs,” J. Computer and Mathematical Sciences, vol.7, no. 1, pp. 13-20, Jan 2016.
[8] V. S. Shigehalli and B. Kenchappa. S, “Some Results On The Reduced Color Energy Of Graphs,” Bulletin Of Mathematics And Statistics Research, vol. 4, no. 4, Oct 2016.
[9] C. Adiga and C. S. S. Swamy, “Bounds on the Largest of Minimum Degree Eigenvalues of Graphs,” Int. Mathematical Forum, vol. 5, no. 37, pp. 1823 – 1831, 2010.
[10] C. Adiga and M. Smitha, “On Maximum Degree Energy of a Graph,” Int. J. Contemp. Math. Sciences, vol. 4, no. 8, pp. 385 – 396, 2009.
[11] A. C. Dinesh and Puttaswamy, “The Minimum Neighbourhood Energy Of A Graph,” Int. Online Multidisciplinary Journal, vol. 5, no. 4, Jan 2016.
[12] A. Alwardi , N. D. Soner and I. Gutman, “On the common-neighborhood energy of a Graph,” Bulletin Classe des sciences mathematiques et natturalles, Jan 2011.
[13] A. N. Al-Kenani, A. Alwardi, O. A. Al-Attas, “On the Non-Common Neighbourhood Energy of Graphs,” Applied Mathematics, 6, pp. 1183-1188, 2015.
[14] P. G. Bhat And S. D’souza, Energy Of Binary Labeled Graphs, Transactions on Combinatorics, vol. 2 no. 3, pp. 53-67, 2013.
[15] M. R. R. Kanna, R Jagadeesh, B. K. Kempegowda, “Minimum Dominating Seidel Energy of a Graph,” Int. J. Scientific & Engineering Research, vol. 7, no. 5, May 2016.
[16] A. M. Naji and N. D. Soner, “The Maximum Eccentricity Energy of a Graph,” Int. J. Scientific & Engineering Research, vol. 7, no. 5, May 2016.
[17] C. Adiga , R. Balakrishnan and W. So, “The skew energy of a digraph, Linear Algebra and its Applications, vol. 432, pp. 1825–1835, 2010.
[18] C. Adiga and M. Smitha, “On the skew Laplacian energy of a digraph,” Int. Mathematical Forum, vol. 4, no. 39, pp. 1907 – 1914, 2009.
[19] H. S. Ramane, H. B. Walikar, S. B. Rao, B. D. Acharya, P. R. Hampiholi, S. R. Jog and I. Gutman, “Equienergetic Graphs,” Kragujevac J. Math. vol. 26, pp. 5-13, 2004.
[20] H. S. Ramane, H. B. Walikar, “Construction Of Equienergetic Graphs,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 57, pp. 203-210, 2007.
[21] G. Indulal, I. Gutman and A. Vijayakumar, On Distance Energy Of Graphs, MATCH Communications in Mathematical and in Computer Chemistry •Jan 2008.
[22] G. Indulal, “Distance Spectrum Of Graph Compositions,”Ars Mathematica Contemporanea, vol. 2, pp. 93–100, 2009.
[23] D. Stevanović, G. Indulal, “The Distance Spectrum And Energy Of The Compositions Of Regular Graphs,” Applied Mathematics Letters, vol. 22, pp. 1136–1140, 2009.
[24] G. Indulal and I. Gutman, “D-Equienergetic Self-Complementary Graphs,” Kragujevac J. Math. vol. 32, pp. 123-131, 2009.
[25] G. Indulal, “The Spectrum of Neighborhood Corona of Graphs,” Kragujevac J. Math. vol. 35, no. 3, pp. 493-500, 2011.
[26] H. B. Walikar and H. S. Ramane, “Energy Of Some Bipartite Cluster Graph, Kragujevac J. Sci. vol. 23, pp. 63-74, 2001.
[27] H. B. Walikar and H. S. Ramane, Energy Of Some Cluster Graphs, Kragujevac Journal of Science, vol. 23, pp. 51 – 62, 2001.
[28] K. Ch. Das, I. Gutman, B. Furtula, On Spectral Radius And Energy Of Extended Adjacency Matrix Of Graphs, Applied Mathematics and Computation vol. 296, pp. 116- 123, 2017.
[29] M. L. Rittenhouse, Properties and Recent Applications in Spectral Graph Theory, Virginia Commonwealth University, 2008
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2021-08-28
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